Linear Algebra and Its Applications · Problem 2.4.35

Vector Spaces — Gilbert Strang

Mathematics · four-fundamental-subspaces

Problem

Suppose

A

is the sum of two matrices of rank one:

A = uv^T + wz^T

. (a) Which vectors span the column space of

A

? (b) Which vectors span the row space of

A

? (c) The rank is less than 2 if \_\_\_\_ or if \_\_\_\_. (d) Compute

A

and its rank if

u = z = (1,0,0)

and

v = w = (0,0,1)